Transcription of Deflections due to Bending - MIT OpenCourseWare
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Deflections due to Bending - MIT OpenCourseWare
------10 Deflections due to Bending The Moment/Curvature Relation Just as we took the pure Bending construction to be accurate enough to produce useful estimates of the normal stress due to Bending for loadings that included shear, so too we will use the same moment/curvature relationship to produce a dif-ferential equation for the transverse displacement , v(x) of the beam at every point along the neutral axis when the Bending moment varies along the beam. Mb EI -sd d = The moment/curvature relation-ship itself is this differential equa-tion. All we need do is express the curvature of the deformed neutral axis in terms of the transverse dis-placement. This is a straight for-ward application of the classical calculus as you have seen perhaps but may also have forgotten.
the constants of integration by evaluating our expression for displacement v(x) and/or our expression for the slope dv/dx at points where we are sure of their val-ues. One such boundary condition is that, at x=0 the displacement is zero, i.e., vx()= 0 x = 0 Another is that, at the support point B, the displacement must vanish, i.e., vx() = 0
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